2182 research outputs found
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Possibilities of Preparing Pupils for Proof Problems of Synthetic Plane Geometry Solvable by Deductive Methods
Full text linkProof problems, especially the ones of the synthetic plane geometry solvable by deductive methods, play a significant role in mathematical education and due to their demanding principle also in the above-standard education including mathematical competitions. Therefore, the issue of preparing pupils for solving the proof problems is very important. This study aimed to find out if the contemporary state of the system of pupils’ preparation for synthetic plane geometry proof problems is sufficient enough for the mentioned purpose. From the full set of schools of the Czech Republic, there were 14 schools identified as the successful ones based on the results of the national round of the Mathematical Olympiad. These schools were asked questions about literature used for pupils’ preparation and the publications named in the answers were then deeply inspected. The results showed a narrow range of the literature used by the schools and the didactic-methodical inspection of stated literature detected considerable space for improvements which led the author to the main theme of his dissertation
Coefficient Bounds for a New Subclasses of Bi-Univalent Functions Associated with Horadam Polynomials
Full text link\In this work we present and investigate three new subclasses of the function class of bi-univalent functions in the open unit disk defined by means of the Horadam polynomials. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients and . Also, we debate Fekete-Szegӧ inequality for functions belongs to these subclasses.
Metallic Ratios : The Mathematical Relationships between different Metallic Means
No full textThis paper introduces the precise mathematical relationships between different Metallic Ratios. Certain distinctive mathematical correlations are found to exist between various Metallic Means. This work presents the empirical formulae those provide the exact mathematical relationships between different Metallic Ratios.  
Metallic Ratios and 3, 6, 9, The Special Significance of Numbers 3, 6, 9 in the Realm of Metallic Meanseans
Full text linkThis work illustrates the intriguing relation between Metallic Means and the Numbers 3, 6 and 9. These numbers occupy special positions in the realm of Metallic Ratios, as elaborated herein
Results on a faster iterative scheme for a generalized monotone asymptotically
Full text linkThis article devoted to present results on convergence of Fibonacci-Halpern scheme (shortly, FH) for monotone asymptotically αn-nonexpansive mapping (shortly, ma αn-n mapping) in partial ordered Banach space (shortly, POB space). Which are auxiliary theorem for demi-close's proof of this type of mappings, weakly convergence of increasing FFH-scheme to a fixed point with aid monotony of a norm and Σn+=∞1 λn= +∞, λn =min{hn , (1-hn)} where hn ⸦ (0,1) where is associated with FH-scheme for an integer n>0 more than that, convergence amounts to be strong by using Kadec-Klee property and finally, prove that this scheme is weak-w2 stable up on suitable status
Some Properties of Chaotic Modified of Bogdanov Map
Full text linkIn this research to the modified dynamics of Bogdanov's map studied, and the found sensitivity to the initial conditions of the modified map found as well as the Lyapunov exponent .the general characteristics of the map by the diffeomorpism. Finally we boosted my research with matlab to find chaotic area
Heat Dissipation Performance of Micro-channel Heat Sink with Various Protrusion Designs
Full text linkThis research will focus on studying the effect of aperture size and shape of the micro-channel heat sink on heat dissipation performance for chip cooling. The micro-channel heat sink is considered to be a porous medium with fluid subject inter-facial convection. Derivation based on energy equation gives a set of governing partial differential equations describing the heat transfer through the micro-channels. Numerical simulation, including steady-state thermal analysis based on CFD software, is used to create a finite element solver to tackle the derived partial differential equations with properly defined boundary conditions related to temperature. After simulating three types of heat sinks with various protrusion designs including micro-channels fins, curly micro-channels fins, and Micro-pin fins, the result shows that the heat sink with the maximum contact area per unit volume will have the best heat dissipation performance, we will interpret the result by using the volume averaging theorem on the porous medium model of the heat sink
Coefficient Bounds and Fekete-Szeg¨o inequality for a Certain Families of Bi-Prestarlike Functions Defined by (M,N)-Lucas Polynomials
Full text linkIn the current work, we use the (M,N)-Lucas Polynomials to introduce a new families of holomorphic and bi-Prestarlike functions defined in the unit disk O and establish upper bounds for the second and third coefficients of the Taylor-Maclaurin series expansions of functions belonging to these families. Also, we debate Fekete-Szeg¨o problem for thesefamilies. Further, we point out several certain special cases for our results
Determination of Pitavastatin Calcium by Analytical Spectrophotometry
Full text linkSimple and rapid spectrophotometric method for the quantitative analysis of Pitavastatin calcium (PTV) in raw material and tablets pharmaceutical formulation has been described. The method is based on the formation of yellow ion-pair complex between Pitavastatin calcium and Bromocresol purple (BCP) in chloroform medium.
Different parameters affecting the reaction such as: effect of solvents, stability, reagent concentration, correlation ratio, etc. were optimized. The formed complex was quantified spectrophotometrically at absorption maximum 405 nm. Linearity range was 2.20 - 35.23 µg/mL, regression analysis showed a good correlation coefficient R2 = 0.9991. The limit of detection (LOD) and limit of quantification (LOQ) were to be 0.367 µg/mL and 1.112 µg/mL respectively. The average percent recovery was found to be (100.62 – 101.14) % for Pitavastatin Calcium. This study was applied on Syrian pharmaceutical trademark: (PAVACRIUM 4 & Londalop). The method was successfully applied for the determination of Pitavastatin calcium in tablets pharmaceutical formulation.
The proposed method is simple, direct, sensitive and do not require any extraction process. Thus, this method could be readily applicable for the quality control and routine analysis
Metallic Means : Beyond the Golden Ratio, New Mathematics and Geometry of all Metallic Ratios based upon Right Triangles, The Formation of the Triples of Metallic Means, And their Classical Correspondence with Pythagorean Triples and p≡1(mod 4) Primes, A
Full text linkThis paper brings together the newly discovered generalised geometry of all Metallic Means and the recently published mathematical formulae those provide the precise correlations between different Metallic Ratios. The paper also puts forward the concept of the “Triples of Metallic Means”. This work also introduces the close correspondence between Metallic Ratios and the Pythagorean Triples as well as Pythagorean Primes. Moreover, this work illustrates the intriguing relationship between Metallic Numbers and the Digits 3 6 9